证明不等式1/(log5(19))+(2/log3(19))+(3/log2(19))
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/01 02:14:33
![证明不等式1/(log5(19))+(2/log3(19))+(3/log2(19))](/uploads/image/z/1587028-4-8.jpg?t=%E8%AF%81%E6%98%8E%E4%B8%8D%E7%AD%89%E5%BC%8F1%2F%28log5%2819%29%29%2B%282%2Flog3%2819%29%29%2B%283%2Flog2%2819%29%29)
证明不等式1/(log5(19))+(2/log3(19))+(3/log2(19))
证明不等式1/(log5(19))+(2/log3(19))+(3/log2(19))<2
证明不等式1/(log5(19))+(2/log3(19))+(3/log2(19))
1/(log5(19))+(2/log3(19))+(3/log2(19))
=log19(5)+2*log19(3)+3*log19(2)
=log19(5*9*8)=log19(360)
这一题用到倒数原理:
1/[logb(a)]=loga(b) 该公式可用换底公式logb(a)=lga/lgb证明
于是原式=log19(360)
不等试左边=log19(5)+log19(9)+log19(8)=log19(360)